Summary: Nonequilibrium time evolution of the spectral function in quantum field theory
Gert Aarts* and Ju¨rgen Berges
Institut fu¨r Theoretische Physik, Philosophenweg 16, 69120 Heidelberg, Germany
Received 19 June 2001; published 17 October 2001
Transport or kinetic equations are often derived assuming a quasiparticle on-shell representation of the
spectral function. We investigate this assumption using a three-loop approximation of the 2PI effective action
in real time, without a gradient expansion or on-shell approximation. For a scalar field in 1 1 dimensions the
nonlinear evolution, including the integration over memory kernels, can be solved numerically. We find that a
spectral function approximately described by a nonzero width emerges dynamically. During the nonequilibrium
time evolution the Wigner transformed spectral function is slowly varying, even in the presence of strong
qualitative changes in the effective particle distribution. These results may be used to make further analytical
progress toward a quantum Boltzmann equation including off-shell effects and a nonzero width.
DOI: 10.1103/PhysRevD.64.105010 PACS number s : 11.10.Wx, 05.60.Gg, 05.70.Ln
I. INTRODUCTION
Current and upcoming heavy-ion experiments at the BNL
Relativistic Heavy Ion Collider RHIC and CERN Large
Hadron Collider LHC have been an important motivation
for an extensive theoretical study of kinetic or transport
equations beyond the level of the classical Boltzmann equa-
tion. In a nonequilibrium environment the quasiparticle